The intermediate level-sets of the four-dimensional membrane model

Xinyi Li; Runsheng Liu

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arXiv · 2205.03621

The intermediate level-sets of the four-dimensional membrane model

Xinyi Li·Runsheng Liu

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Abstract

In this paper, we consider the discrete membrane model in four dimensions. We confirm the existence of the scaling limit of the intermediate (i.e., a multiple of the expected maximum) level-sets of the model, and show that it is equal in law to the sub-critical Gaussian multiplicative chaos (GMC) measure of the continuum membrane model.

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Xinyi Li, Runsheng Liu. 2022-05-07. The intermediate level-sets of the four-dimensional membrane model. https://arxiv.org/abs/2205.03621

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